/*
 * Copyright 2010-2012 Susanta Tewari. <freecode4susant@users.sourceforge.net>
 *
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program.  If not, see <http://www.gnu.org/licenses/>.
 */

package bd.org.apache.commons.math.distribution;

import bd.org.apache.commons.math.exception.NotStrictlyPositiveException;
import bd.org.apache.commons.math.exception.util.LocalizedFormats;
import bd.org.apache.commons.math.special.Beta;
import bd.org.apache.commons.math.special.Gamma;
import bd.org.apache.commons.math.util.FastMath;

/**
 * Implementation of Student's t-distribution.
 *
 * @version $Id: TDistribution.java 1244107 2012-02-14 16:17:55Z erans $
 * @see "<a href='http://en.wikipedia.org/wiki/Student&apos;s_t-distribution'>Student's t-distribution (Wikipedia)</a>"
 * @see "<a href='http://mathworld.wolfram.com/Studentst-Distribution.html'>Student's t-distribution (MathWorld)</a>"
 */
public class TDistribution extends AbstractRealDistribution {

    /**
     * Default inverse cumulative probability accuracy.
     *
     * @since 2.1
     */
    public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;

    /**
     * Serializable version identifier
     */
    private static final long serialVersionUID = -5852615386664158222L;

    /**
     * The degrees of freedom.
     */
    private final double degreesOfFreedom;

    /**
     * Inverse cumulative probability accuracy.
     */
    private final double solverAbsoluteAccuracy;

    /**
     * Create a t distribution using the given degrees of freedom.
     *
     * @param degreesOfFreedom Degrees of freedom.
     * @throws NotStrictlyPositiveException if {@code degreesOfFreedom <= 0}
     */
    public TDistribution(double degreesOfFreedom) throws NotStrictlyPositiveException {

        this(degreesOfFreedom, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    }

    /**
     * Create a t distribution using the given degrees of freedom and the
     * specified inverse cumulative probability absolute accuracy.
     *
     * @param degreesOfFreedom Degrees of freedom.
     * @param inverseCumAccuracy the maximum absolute error in inverse
     * cumulative probability estimates
     * (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
     * @throws NotStrictlyPositiveException if {@code degreesOfFreedom <= 0}
     * @since 2.1
     */
    public TDistribution(double degreesOfFreedom, double inverseCumAccuracy)
            throws NotStrictlyPositiveException {

        if (degreesOfFreedom <= 0) {

            throw new NotStrictlyPositiveException(LocalizedFormats.DEGREES_OF_FREEDOM,
                    degreesOfFreedom);
        }

        this.degreesOfFreedom  = degreesOfFreedom;
        solverAbsoluteAccuracy = inverseCumAccuracy;
    }

    /**
     * Access the degrees of freedom.
     *
     * @return the degrees of freedom.
     */
    public double getDegreesOfFreedom() {

        return degreesOfFreedom;
    }


    /**
     * {@inheritDoc}
     * For this distribution {@code P(X = x)} always evaluates to 0.
     *
     * @return 0
     */
    @Override
    public double probability(double x) {

        return 0.0;
    }


    /**
     * {@inheritDoc}
     */
    @Override
    public double density(double x) {

        final double n           = degreesOfFreedom;
        final double nPlus1Over2 = (n + 1) / 2;

        return FastMath.exp(Gamma.logGamma(nPlus1Over2)
                            - 0.5 * (FastMath.log(FastMath.PI) + FastMath.log(n))
                            - Gamma.logGamma(n / 2) - nPlus1Over2 * FastMath.log(1 + x * x / n));
    }


    /**
     * {@inheritDoc}
     */
    @Override
    public double cumulativeProbability(double x) {

        double ret;

        if (x == 0) {
            ret = 0.5;
        } else {

            double t = Beta.regularizedBeta(degreesOfFreedom / (degreesOfFreedom + (x * x)),
                                            0.5 * degreesOfFreedom, 0.5);

            if (x < 0.0) {
                ret = 0.5 * t;
            } else {
                ret = 1.0 - 0.5 * t;
            }
        }

        return ret;
    }


    /**
     * {@inheritDoc}
     */
    @Override
    protected double getSolverAbsoluteAccuracy() {

        return solverAbsoluteAccuracy;
    }


    /**
     * {@inheritDoc}
     * For degrees of freedom parameter {@code df}, the mean is
     * <ul>
     * <li>if {@code df > 1} then {@code 0},</li>
     * <li>else undefined ({@code Double.NaN}).</li>
     * </ul>
     */
    @Override
    public double getNumericalMean() {

        final double df = getDegreesOfFreedom();

        if (df > 1) {
            return 0;
        }

        return Double.NaN;
    }


    /**
     * {@inheritDoc}
     * For degrees of freedom parameter {@code df}, the variance is
     * <ul>
     * <li>if {@code df > 2} then {@code df / (df - 2)},</li>
     * <li>if {@code 1 < df <= 2} then positive infinity
     * ({@code Double.POSITIVE_INFINITY}),</li>
     * <li>else undefined ({@code Double.NaN}).</li>
     * </ul>
     */
    @Override
    public double getNumericalVariance() {

        final double df = getDegreesOfFreedom();

        if (df > 2) {
            return df / (df - 2);
        }

        if ((df > 1) && (df <= 2)) {
            return Double.POSITIVE_INFINITY;
        }

        return Double.NaN;
    }


    /**
     * {@inheritDoc}
     * The lower bound of the support is always negative infinity no matter the
     * parameters.
     *
     * @return lower bound of the support (always
     *         {@code Double.NEGATIVE_INFINITY})
     */
    @Override
    public double getSupportLowerBound() {

        return Double.NEGATIVE_INFINITY;
    }


    /**
     * {@inheritDoc}
     * The upper bound of the support is always positive infinity no matter the
     * parameters.
     *
     * @return upper bound of the support (always
     *         {@code Double.POSITIVE_INFINITY})
     */
    @Override
    public double getSupportUpperBound() {

        return Double.POSITIVE_INFINITY;
    }


    /**
     * {@inheritDoc}
     */
    @Override
    public boolean isSupportLowerBoundInclusive() {

        return false;
    }


    /**
     * {@inheritDoc}
     */
    @Override
    public boolean isSupportUpperBoundInclusive() {

        return false;
    }


    /**
     * {@inheritDoc}
     * The support of this distribution is connected.
     *
     * @return {@code true}
     */
    @Override
    public boolean isSupportConnected() {

        return true;
    }
}
